# [EM] condorcet loser elimination PR

Dgamble997 at aol.com Dgamble997 at aol.com
Tue Jul 22 17:58:04 PDT 2003

```Alex Small wrote in part:

"1) Elect the Condorcet winner, or the winner of the Condorcet completion
method (from now on I'll use "CW" to denote either the Condorcet winner or
the winner of the Condorcet completion method, just to be succinct).

2) As in STV or PAV (Proportional Approval Voting) after electing
somebody we need to reduce the weight of some of the ballots. In STV we
would reduce the weight of all ballots that ranked the candidate first
(first among those remaining, that is). In Proportional Condorcet (PC) we
would reduce the weight of any ballots that prefer the most recently
elected candidate to the runner-up.

Who is the runner-up? Whoever the CW would have been had the most
recently elected candidate (i.e. the most recent CW) not been on the
ballot. This is NOT the Condorcet Loser, at least not as I understand the
term. I always think of the Condorcet Loser as whoever loses ALL pairwise
contests (if such a candidate exists). I guess you could say that any
candidate not elected is a Condorcet Loser, but then the Condorcet Loser
is just a loser, and there's no need for a special term."

Alex, using a Droop quota to elect 3 from the 4 candidates given below who
would be elected under your method?

27 A1>A2>B
26 A2>A1>B
7 B>A1>A2
6 B>C
34 C>B

First Count

A1   27
A2   26
B     13
C     34

Any good ( in my opinion)  method should elect A1, A2 and C who all have a
Droop quota of first preference votes.

On the first count A1 is the Condorcet winner and is elected. A1's 27 votes
are now reduced to a value of  0.074 and transferred giving for the second
count

A2 27.998
B   13
C   34

B is now the Condorcet winner (B v A2, 47 v 27.998; B v C 40.998 v 34) and
elected. C is the Condorcet runner up. Presumably since the  A2 votes prefer B
to C some of these votes are transferred at a reduced value to elect B.

C wins the final seat against A2.

Am I misunderstanding your method or does it allow the defeat of candidates
who have obtained a quota of first preference votes?

David Gamble

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